Power and Voltage Problem?

Question

If the voltage across a device is v(t) = 5cos(10t) V and the current through is i(t) = 0.5sin(10t) A, what is the device power at t = 0.2s and t = 0.4s?

I tried just plugging in the 2 different values, and multiplying them together (p = vi), but that seems too simple.

Is this a problem where I would first have to integrate v(t) and i(t) as well?

Thanks

Answer 1

You are correct. Instantaneous power is simply v(t) * i(t) at time 't'.

Now, if they ask you what the average power is, or the RMS power, or the peak power, *then* you have to do a little more math.

.

Answer 2

As stated before, you are correct for finding the power at a single specific time. The signal frequency of 10 cycles/s or most likely 10 rad/s does not matter in this case.

If you wanted to calculate the net power dissipated over a time period then yes you would integrate the voltage and current signals independently over the time period and multiply the two
OR
you could use one integral with the integrand being the product of the two over the time period. My $0.02